Associative memories and associative processing as described in U.S. Pat. Nos. 5,942,002; 5,742,611; 6,157,617: 6,617,400; and U.S. patent application Nos. 09/419,217; 09/672,754; 09/768,102; 09/767,797; 09/768,101; 09/767,493 all assigned to the same assignee as the present application, require transform generators (polynomial code generators). As explained in the above referenced patents (patent applications) a transform (polynomial code) is generated for use in an associative memory. The polynomial generator is generally applied to a key to determine an address (transform, CRC, remainder, code) in a memory where information relating to the key is stored. In the above applications the transform (CRC, remainder) is broken into an address and a confirmer. The confirmer is used to resolve collisions between two distinct items that might otherwise have the same address. In addition to associative memory applications, associative processing applications are described in the above referenced patents (patent applications). Both of these applications require the fast and efficient generation of transforms (polynomial codes). Two general methods of polynomial code generators are known. One is using linear feedback shift registers to perform the division modulo two on a bit by bit basis. There have been some efficiencies realized in the general process, but the basic idea is the same. The other method involves a table lookup process. This method has generally been limited to a byte by byte process. This is because the lookup table for a byte range of number is 256 (28) entries. If the table were to be expanded for two bytes the number of entries would be 65,536 entries. Obviously a table this large is slow are requires a lot of memory. Despite this there is a need for a two bytes by two bytes process when oriental symbols encoded, such as used in Japan and China. All the potential symbols in these languages cannot be encoded by a single byte. Another use for more than one byte at a time is for computers that now have 64 bit words.
Thus there exists a need for an improved method and system for generating a transform (polynomial code, CRC) that is faster and more efficient than previous systems and methods.